Finite Group DatabasebetaFinite Group DatabasebetaOrder 33516.
156 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #26013905 |
| commutator, hypocenter | C72×C19 | C22×C9 |
| Fitting, socle, cosocle | C3×C72×C19 | C22×C3 |
| prime radical | C3×C7×D7×D19 | C3 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #30660599 | C2 | semidirect |
| 2. #30660584 | C2 | semidirect |
| 3. #30660582 | C2 | semidirect |
| 5. #22552709 | C22 | semidirect |
| 11. C7×D7×D19 | C9 | semidirect |
| 20. C7×D133 | C2×C9 | semidirect |
| 21. C7×D7×C19 | C2×C9 | semidirect |
| 22. C72×D19 | C2×C9 | semidirect |
| 29. C72×C19 | C22×C9 | semidirect |
| 43. D7×D19 | C7⋊C9 | semidirect |
| 55. D133 | C2×C7⋊C9 | semidirect |
| 58. C7×D19 | D7⋊C9 | semidirect |
| 59. C7×D19 | C2×C7⋊C9 | semidirect |
| 60. D7×C19 | C2×C7⋊C9 | semidirect |
| 68. C7×C19 | C2×D7⋊C9 | semidirect |
| 69. C7×C19 | C22×C7⋊C9 | semidirect |
| 82. C7×D7 | #4294⋊C2 | semidirect |
| 90. C72 | C2×#4294⋊C2 | semidirect |
| 100. D19 | #11725076 | semidirect |
| 107. C19 | C2×#11725076 | semidirect |
| 117. D7 | #14558780 | semidirect |
| 121. C7 | #14558780⋊C2 | semidirect |
| 122. C7 | C2×#14558780 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30660599 | 2 |
| #30660584 | 2 |
| #30660582 | 2 |
| C3×C7×D7×D19 | 3 |
| C2×#14558780 | 7 |
| #14558780⋊C2 | 7 |
| C2×#11725076 | 19 |